Abstract
The global Markov property (GMP) has been shown in various cases under various conditions by quite different methods. Here we investigate the problem of the GMP (for lattice spin systems) from the nonstandard point of view. By embedding the given system into a hyperfinite system we are able to approximate the conditional expectations that are involved in the formulation of the GMP by internal conditional expectations. This leads to a nonstandard equivalent to the GMP as well as to sufficient nonstandard conditions that are easy to formulate. Finally, we then determine the interrelations between these conditions and some of the standard criteria, thus making their relative position somewhat clearer.
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Kessler, C. Nonstandard conditions for the global Markov property for lattice fields. Acta Appl Math 7, 225–256 (1986). https://doi.org/10.1007/BF00047094
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DOI: https://doi.org/10.1007/BF00047094